The radius of the circle with center at the origin is 10 units. Write the coordinates of the point where the circle intersects the axes. Find the distance between any two of such points.

Formula used:

Let the point be A (x, 0) and B (0, y)

Given center O (0, 0) and radius = 10

Distance of OA

⇒ 5 = √ ((x – 0)² + (0 – 0)²)

⇒ 5 = √ ((x)² + (0)²)

⇒ 5= √ (x² + 0)

⇒ 5 = √ x²

⇒ 5 = x

∴ point A is (5, 0)

Distance of OB

⇒ 5 = √ ((0 – 0)² + (y – 0)²)

⇒ 5 = √ ((0)² + (y)²)

⇒ 5 = √ (0 + y²)

⇒ 5 = √ y²

⇒ 5 = y

∴ point B is (0, 5)

Now,

Distance AB = √ ((0 – 5)² + (5 – 0)²)

= √ ((–5)² + (5)²)

= √ (25 + 25)

= √ (50)

= 5√2